A uniform electric field of magnitude 2.80×104 makes an angle of 37 with a plane surface of area 1.60×10−2 .What is the electric flux through this surface?
To find the electric flux through a surface, you can use the formula:
Electric Flux = Electric Field * Surface Area * Cosine(angle between the electric field and the surface)
In this case, the electric field magnitude is given as 2.80×10^4, the surface area is given as 1.60×10^−2, and the angle between the electric field and the surface is given as 37 degrees.
First, let's convert the angle from degrees to radians. Since the cosine function requires the angle to be in radians, we use the formula:
Angle in radians = Angle in degrees * π / 180
So, the angle in radians is:
37 degrees * π / 180 ≈ 0.6458 radians
Now, we can calculate the electric flux using the formula:
Electric Flux = 2.80×10^4 * 1.60×10^−2 * Cos(0.6458)
Calculating the cosine value for 0.6458 radians, we find:
Cos(0.6458) ≈ 0.784
Substituting this value into the formula, we get:
Electric Flux ≈ 2.80×10^4 * 1.60×10^−2 * 0.784
Calculating this expression, we find:
Electric Flux ≈ 702.464
Therefore, the electric flux through the surface is approximately 702.464.